1. Field of the Invention
The invention relates to a method and apparatus for calibrating spectral radiometers, in particular Fourier spectrometers (i.e. Michelson interferometers) with the aid of black radiators, preferably in the infrared spectral range.
2. Description of the Prior Art
Spectral radiometers, which will be referred to for simplicity hereinafter as "spectrometers", are employed inter alia also for measuring absolute radiation quantities, such as the "spectral radiance" or the "spectral radiant intensity". Absolute radiation quantities are the requirement for derivatives made therefrom of other absolute quantities, for example temperature, emittance or concentrations of the components of gas mixtures. Such absolute radiation quantities are obtained from the measuring signals of the spectrometers via a calibration.
The measuring signal of a spectrometer, i.e. the measured spectrum thereof, can be described by the following equation: EQU S(.nu.)=.tau.(.nu.) R(.nu.) (L(.nu.)+G(.nu.)) (1)
where .nu. denotes the wave number, .tau.(.nu.) the spectral transmittance of the atmosphere between spectrometer and measured object, S(.nu.) a measured spectrum, R(.nu.) the spectral sensitivity of the spectrometer, L(.nu.) the spectral radiance of the object and G(.nu.) the effective spectral radiance of the spectrometer housing (inner). The spectral radiance L(.nu.) of the measured object is obtained by transformation as: ##EQU1## Quantitatively, the spectral radiance L(.nu.) of the object can be determined only when the values of .tau.(.nu.), R (.nu.) and G(.nu.) are known. Whereas the spectral transmittance .tau.(.nu.) of the atmosphere varies with time and location and depends on the length of the measurement distance, the spectrometer's spectral sensitivity R (.nu.) and the effective spectral radiance of the spectrometer housing G(.nu.) are measuring apparatus parameters and thus to be treated as quantities which are constant during finite periods of time. To determine the radiance of a measured object the spectral transmittance .tau.(.nu.) of the atmosphere is determined from additional measurements whilst the apparatus parameters R (.nu.) and G(.nu.) result from the calibration.
As described by B. J. Vastag, S. R. Horman in the article "Calibration of a Michelson interferometer spectrometer" in SPIE Vol 289 1981, Fourier Transform Infrared Spectroscopy (1981), the hitherto usual calibration is carried out by means of black body radiators at two different temperatures in accordance with the relationship given below (the calibration likewise used at only one temperature is expedient only in a few specific cases and will consequently not be considered in detail below): EQU S.sub.h (.nu..sub.i)=R(.nu..sub.i)(L(.nu..sub.i, T.sub.h)+G(.nu..sub.i))(3)
where T.sub.h denotes the temperature of a calibrating radiator. For i=1, 2, 3 . . . ,n and for h=1, 2 all apparatus parameters R(.nu.) and G(.nu.) can be determined therefrom, on condition that the temperatures T.sub.h are known. The temperatures are measured via contact sensors in the interior or on the surface of the black body radiators. For such a radiance calibration extended area radiators are used having an area completely covering that of the aperture of the spectrometer. Usual areas are areas having edge lengths of 10 cm.times.10 cm to 60 cm.times.60 cm. The radiators are arranged perpendicularly to the surface of the earth because the optical axis of the spectrometers are usually aligned parallel to the earth surface; slight deviations are adjustable downwardly and correspondingly large deviations upwardly.
The two temperatures T.sub.h of the calibrating radiators are set so that the radiation intensity to be expected, i.e. the radiance or radiant intensity of the measured object, lies between the radiation intensities of the two radiators.
In this conventional calibration the transmittance .tau.(.nu.) of the atmosphere is assumed to be negligible or the ranges in which the transmittance is not negligible are excluded and interpolated in the calibration spectra.
If the spectrometer is a Fourier transform spectrometer (FTS), the primary measuring signal thereof is a so-called "interferogram" which is transferred by a mathematical Fourier transformation to a secondary measuring signal, the (uncalibrated) spectrum. Due to the measuring method the interferogram is an asymmetrical function; it thus provides on Fourier transformation a complex spectrum consisting of real and imaginary component or magnitude and phase. In reality of course the spectrum of the radiation is real; from the complex spectrum the real amount spectrum is therefore determined and then further employed.
Disadvantageous with this calibrating method is that
1. the black radiators are perpendicularly upright and thus subject to convection, the surface temperatures thereof therefore having a gradient of a few Kelvin from the lower edge to the upper edge;
2. the temperature of the black body radiators are measured via (error-prone) contact sensors;
3. the transmittance .tau.(.nu.) of the atmosphere is not detected and must be determined by additional measurements and
4. in the calculation of amount or absolute value spectra of the apparatus parameters R(.nu..sub.i) and G(.nu..sub.i) for determining spectral radiances of the measured objects the information on the phase is no longer contained. This can then lead to an incorrect sign of the spectra or individual points of the spectra, particularly when the temperature and the radiance of the measured object is less than the temperature or radiance of the spectrometer, this leading to a reversal of the radiation flux. Also, such errors can possibly occur by any transit time differences present in the electronics of the interferometer, caused for example by the phase response of the electrical filters necessary.